C₂×D₈₃₂₅ #45685779

order	33300
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₁₆₆₅₀
direct product	C₂×D₈₃₂₅
unambiguous semidirect product	(C₂×C₉)⋊D₉₂₅
unambiguous semidirect product	(C₂×C₂₅)⋊D₃₃₃
unambiguous semidirect product	(C₂×C₃₇)⋊D₂₂₅

Splittings

Fitting	C₂×C₉×C₂₅×C₃₇ ⋊ C₂
derived, Hall	C₉×C₂₅×C₃₇ ⋊ C₂²
Hall	C₂₅×C₃₇ ⋊ C₂×D₉
Hall	C₉×C₃₇ ⋊ C₂×D₂₅
Hall	C₉×C₂₅ ⋊ C₂×D₃₇
Sylow	C₃₇ ⋊ C₂×D₂₂₅
Sylow	C₂₅ ⋊ C₂×D₃₃₃
Sylow	C₉ ⋊ C₂×D₉₂₅

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₈₃₂₅
commutator, cosocle, hypocenter	C₉×C₂₅×C₃₇	C₂²
Frattini	C₃×C₅	C₂×D₅₅₅
Fitting	C₂×C₉×C₂₅×C₃₇	C₂
socle	C₂×C₃×C₅×C₃₇	D₁₅
LCS	G ▷ C₉×C₂₅×C₃₇
UCS	C₁ ◁ C₂

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 73
transitive degree	μ_t(G) = 16650

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

Conjugacy classes & character table

8328 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33300, 52);

C2×D8325 #45685779