Finite Group Databasebeta

C2×#27161154 #38751396

order25216
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#27161154

Splittings

FittingC2×C22⋊C8×C197 ⋊ C2
SylowC197 ⋊ C2×#436

Subgroups

subgroupG/H
centerC22×C4C22×D197
commutatorC22×C197C23×C4
FrattiniC2×C4C23×D197
FittingC2×C22⋊C8×C197C2
socleC23×C197C22×C4
prime radicalC22×C22⋊D197C4
cosocleC2×C4×C197C24
hypercenterC2×C22⋊C8D197
hypocenterC197C2×#436
LCSG ▷ C22×C197 ▷ C197
UCSC1 ◁ C22×C4 ◁ C2×C22⋊C8

552 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, 13194);