Finite Group Databasebeta

C2×#27159375 #38734620

order24896
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C24

Aliases

direct productC2×#27159375

Splittings

SylowC389 ⋊ C2×#125

Subgroups

subgroupG/H
centerC23C22×D389
commutator, cosocleC22×C389C24
FrattiniC22C23×D389
FittingC2×C4⋊C4×C389C2
socle, prime radicalC23×C389C23
hypercenterC2×C4⋊C4D389
hypocenterC389C2×#125
LCSG ▷ C22×C389 ▷ C389
UCSC1 ◁ C23 ◁ C2×C4⋊C4

226 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 24896

Conjugacy classes & character table

3908 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24896, 1070);