C₂×D₉₂₂₅ #49146641

order	36900
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₁₈₄₅₀
direct product	C₂×D₉₂₂₅
unambiguous semidirect product	(C₂×C₉)⋊D₁₀₂₅
unambiguous semidirect product	(C₂×C₂₅)⋊D₃₆₉
unambiguous semidirect product	(C₂×C₄₁)⋊D₂₂₅

Splittings

Fitting	C₂×C₉×C₂₅×C₄₁ ⋊ C₂
derived, Hall	C₉×C₂₅×C₄₁ ⋊ C₂²
Hall	C₂₅×C₄₁ ⋊ C₂×D₉
Hall	C₉×C₄₁ ⋊ C₂×D₂₅
Hall	C₉×C₂₅ ⋊ C₂×D₄₁
Sylow	C₄₁ ⋊ C₂×D₂₂₅
Sylow	C₂₅ ⋊ C₂×D₃₆₉
Sylow	C₉ ⋊ C₂×D₁₀₂₅

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₉₂₂₅
commutator, cosocle, hypocenter	C₉×C₂₅×C₄₁	C₂²
Frattini	C₃×C₅	C₂×D₆₁₅
Fitting	C₂×C₉×C₂₅×C₄₁	C₂
socle	C₂×C₃×C₅×C₄₁	D₁₅
LCS	G ▷ C₉×C₂₅×C₄₁
UCS	C₁ ◁ C₂

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 77
transitive degree	μ_t(G) = 18450

A minimal faithful permutation representation — 2 generators on 77 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)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77);(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)(38,77)(39,76)(40,75)(41,74)(42,73)(43,72)(44,71)(45,70)(46,69)(47,68)(48,67)(49,66)(50,65)(51,64)(52,63)(53,62)(54,61)(55,60)(56,59)(57,58)

Conjugacy classes & character table

9228 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36900, 42);

C2×D9225 #49146641