Finite Group Databasebeta

C2×#27159472 #38735176

order24896
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#27159472

Splittings

SylowC389 ⋊ C2×#131

Subgroups

subgroupG/H
centerC22C22×#13095555
commutatorC2×C389C23×C4
FrattiniC2C23×#13095555
FittingC2×Q8×C389C4
socleC22×C389C22×C4
prime radicalC2×#20261967C2
cosocleDic389C24
hypercenterC2×Q8#13095555
hypocenterC389C2×#131
LCSG ▷ C2×C389 ▷ C389
UCSC1 ◁ C22 ◁ C2×Q8

266 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12448

Conjugacy classes & character table

1010 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24896, 1626);