C₂×D₆₅₂₅ #39907802

order	26100
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₁₃₀₅₀
direct product	C₂×D₆₅₂₅
unambiguous semidirect product	(C₂×C₉)⋊D₇₂₅
unambiguous semidirect product	(C₂×C₂₅)⋊D₂₆₁
unambiguous semidirect product	(C₂×C₂₉)⋊D₂₂₅

Splittings

Fitting	C₂×C₉×C₂₅×C₂₉ ⋊ C₂
derived, Hall	C₉×C₂₅×C₂₉ ⋊ C₂²
Hall	C₂₅×C₂₉ ⋊ C₂×D₉
Hall	C₉×C₂₉ ⋊ C₂×D₂₅
Hall	C₉×C₂₅ ⋊ C₂×D₂₉
Sylow	C₂₉ ⋊ C₂×D₂₂₅
Sylow	C₂₅ ⋊ C₂×D₂₆₁
Sylow	C₉ ⋊ C₂×D₇₂₅

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₆₅₂₅
commutator, cosocle, hypocenter	C₉×C₂₅×C₂₉	C₂²
Frattini	C₃×C₅	C₂×D₄₃₅
Fitting	C₂×C₉×C₂₅×C₂₉	C₂
socle	C₂×C₃×C₅×C₂₉	D₁₅
LCS	G ▷ C₉×C₂₅×C₂₉
UCS	C₁ ◁ C₂

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 65
transitive degree	μ_t(G) = 13050

A minimal faithful permutation representation — 2 generators on 65 points:

(1,2)(3,4,5,6,7,8,9,10,11)(12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65);(4,11)(5,10)(6,9)(7,8)(13,36)(14,35)(15,34)(16,33)(17,32)(18,31)(19,30)(20,29)(21,28)(22,27)(23,26)(24,25)(38,65)(39,64)(40,63)(41,62)(42,61)(43,60)(44,59)(45,58)(46,57)(47,56)(48,55)(49,54)(50,53)(51,52)

Conjugacy classes & character table

6528 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₂₆₁₀₀
maximal normal subgroup of	D₂₆₁₀₀
maximal quotient of	Dic₁₃₀₅₀, D₂₆₁₀₀

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26100, 36);

C2×D6525 #39907802