Finite Group Databasebeta

C2×#27159295 #38734048

order24896
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23

Aliases

direct productC2×#27159295

Splittings

SylowC389 ⋊ C2×#97

Subgroups

subgroupG/H
centerC22×C4C2×D389
commutatorC2×C389C2×C42
FrattiniC2×C4C22×D389
FittingC2×C42×C389C2
socle, prime radicalC23×C389C2×C4
cosocleC2×C4×C389C23
hypercenterC2×C42D389
hypocenterC389C2×#97
LCSG ▷ C2×C389 ▷ C389
UCSC1 ◁ C22×C4 ◁ C2×C42

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 24896

Conjugacy classes & character table

6248 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24896, 498);