Finite Group Databasebeta

C2×#27159316 #38734130

order24896
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#27159316

Splittings

SylowC389 ⋊ C2×#106

Subgroups

subgroupG/H
centerC23D1556
commutatorC4×C389C22×C4
FrattiniC2×C4C22×D389
FittingC22×C8×C389C2
socle, prime radicalC23×C389D4
cosocleC2×C4×C389C23
hypercenterC22×C8D389
hypocenterC389C2×#106
LCSG ▷ C4×C389 ▷ C2×C389 ▷ C389
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

130 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 24896

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, 580);