Finite Group Databasebeta

C2×#27159451 #38735101

order24896
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productC2×#27159451

Splittings

SylowC389 ⋊ C2×C4⋊C8

Subgroups

subgroupG/H
centerC23C2×#13095555
commutatorC2×C389C22×C8
FrattiniC22C22×#13095555
FittingC22×C4×C389C4
socle, prime radicalC23×C389C2×C4
cosocleC2×Dic389C23
hypercenterC22×C4#13095555
hypocenterC389C2×C4⋊C8
LCSG ▷ C2×C389 ▷ C389
UCSC1 ◁ C23 ◁ C22×C4

138 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 24896

Conjugacy classes & character table

1592 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24896, 1551);