Finite Group Databasebeta

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Cayley diagram

C2×C4×D25 #87742

order400
isoclinismisoclinic class of D25
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×C4×D25

Splittings

FittingC2×C4×C25 ⋊ C2
derived, SylowC25 ⋊ C22×C4

Subgroups

subgroupG/H
center, hypercenterC2×C4D25
commutator, hypocenterC25C22×C4
FrattiniC2×C5C22×D5
FittingC2×C4×C25C2
socleC22×C5C2×D5
prime radicalC22×D25C2
cosocleC2×C25C23
LCSG ▷ C25
UCSC1 ◁ C2×C4

81 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 31
transitive degreeμt(G) = 200

A minimal faithful permutation representation — 3 generators on 31 points:

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

Conjugacy classes & character table

112 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11716368, #11716418, (C2×#1035)⋊C4, …
maximal normal subgroup of#11716368, #11716418, (C2×#1035)⋊C4, …
maximal quotient ofC4×Dic50, C42×D25, #11716434, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 36);