Finite Group Databasebeta

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C4×#20263321 #38745265

order25216
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productC4×#20263321

Splittings

FittingC4×C4⋊C4×C197 ⋊ C2
SylowC197 ⋊ C4×#126

Subgroups

subgroupG/H
centerC22×C4C22×D197
commutatorC22×C197C23×C4
FrattiniC23C23×D197
FittingC4×C4⋊C4×C197C2
socle, cosocleC23×C197C24
prime radicalC23×D197C23
hypercenterC4×C4⋊C4D197
hypocenterC197C4×#126
LCSG ▷ C22×C197 ▷ C197
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

516 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12608

Conjugacy classes & character table

3976 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25216, 7063);