Finite Group Databasebeta

C2×#27159301 #38734076

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

Aliases

direct productC2×#27159301

Splittings

SylowC389 ⋊ C2×#100

Subgroups

subgroupG/H
centerC22C22⋊Dic389
commutatorC22×C389C22×C4
FrattiniC2×C4C22×D389
Fitting, prime radicalC22×D4×C389C2
socleC22×C389C22⋊C4
cosocleC2×C4×C389C23
hypercenterC22×D4D389
hypocenterC389C2×#100
LCSG ▷ C22×C389 ▷ C2×C389 ▷ C389
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

186 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6224

Conjugacy classes & character table

3902 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24896, 526);