Finite Group Databasebeta

C2×#27159330 #38734526

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

Aliases

direct productC2×#27159330

Splittings

SylowC389 ⋊ C2×Q32

Subgroups

subgroupG/H
centerC22#20261951
commutator, cosocleC8×C389C23
FrattiniC8C22×D389
FittingC2×Q16×C389C2
socle, prime radicalC22×C389D8
hypercenterC2×Q16D389
hypocenterC389C2×Q32
LCSG ▷ C8×C389 ▷ C4×C389 ▷ C2×C389 ▷ C389
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

82 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 24896

Conjugacy classes & character table

2738 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24896, 976);