C₃₇×Dic₂₅ #16814848

order	3700
isoclinism	isoclinic class of D₂₅
automorphism	?
homology	Abelianization (H₁) = C₄×C₃₇ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₃₇×Dic₂₅

Splittings

derived, Sylow	C₂₅ ⋊ C₄×C₃₇
Hall	C₂₅×C₃₇ ⋊ C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃₇	D₂₅
commutator, hypocenter	C₂₅	C₄×C₃₇
Frattini	C₂×C₅	D₅×C₃₇
Fitting	C₂×C₂₅×C₃₇	C₂
socle, prime radical	C₂×C₅×C₃₇	D₅
cosocle	C₂×C₂₅	C₂×C₃₇
LCS	G ▷ C₂₅
UCS	C₁ ◁ C₂×C₃₇

18 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 66
transitive degree	μ_t(G) = 3700

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

Conjugacy classes & character table

1036 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	Dic₂₅×C₃₇⋊C₃, C₃×C₃₇×Dic₂₅, C₃₇×Dic₇₅, …
maximal normal subgroup of	Dic₂₅×C₃₇⋊C₃, C₃×C₃₇×Dic₂₅, C₇×C₃₇×Dic₂₅
maximal quotient of	C₃×C₃₇×Dic₂₅, C₃₇×Dic₇₅, C₇×C₃₇×Dic₂₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3700, 2);

C37×Dic25 #16814848