C₄×Dic₂₅ #87717

order	400
isoclinism	isoclinic class of D₂₅
automorphism	?
homology	Abelianization (H₁) = C₄² · Schur multiplier (H₂) = C₄

Aliases

direct product

C₄×Dic₂₅

Splittings

derived, Sylow

C₂₅ ⋊ C₄²

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₄	D₂₅
commutator, hypocenter	C₂₅	C₄²
Frattini, socle, prime radical	C₂²×C₅	C₂×D₅
Fitting	C₂×C₄×C₂₅	C₂
cosocle	C₂²×C₂₅	C₂²
LCS	G ▷ C₂₅
UCS	C₁ ◁ C₂×C₄

45 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 33
transitive degree	μ_t(G) = 400

A minimal faithful permutation representation — 2 generators on 33 points:

(2,4)(3,7)(5,10)(6,13)(8,16)(9,15)(11,12)(14,20)(17,21)(18,22)(19,24)(23,25)(30,31,32,33);(1,15,25,18,4,7,21,19,10,13,16,14,12,11,20,8,6,5,24,17,3,2,22,23,9)(26,27,28,29)

Conjugacy classes & character table

112 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₈×Dic₂₅, #11716363, #11716364, …
maximal normal subgroup of	C₈×Dic₂₅, #11716363, #11716364, …
maximal quotient of	C₄×#6014, #11716351, C₈×Dic₂₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 11);

C4×Dic25 #87717

Aliases

Splittings

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₄×Dic₂₅ #87717