Finite Group Databasebeta

C2×#27159454 #38735111

order24896
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×#27159454

Splittings

SylowC389 ⋊ C2×#108

Subgroups

subgroupG/H
centerC22C4⋊#13095555
commutatorC4×C389C22×C4
FrattiniC4C22×#13095555
FittingC2×C8×C389C4
socleC22×C389C4⋊C4
prime radicalC22×D389Q8
cosocleC4×D389C23
hypercenterC2×C8#13095555
hypocenterC389C2×#108
LCSG ▷ C4×C389 ▷ C2×C389 ▷ C389
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12448

Conjugacy classes & character table

1580 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24896, 1561);