Finite Group Databasebeta

C2×#27159320 #38734145

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

Aliases

direct productC2×#27159320

Splittings

SylowC389 ⋊ C2×#108

Subgroups

subgroupG/H
centerC2×C4D1556
commutatorC4×C389C22×C4
FrattiniC2×C4C22×D389
FittingC22×C8×C389C2
socleC22×C389C4⋊C4
prime radicalC23×C389Q8
cosocleC2×C4×C389C23
hypercenterC22×C8D389
hypocenterC389C2×#108
LCSG ▷ C4×C389 ▷ C2×C389 ▷ C389
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12448

Conjugacy classes & character table

6236 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24896, 595);