Finite Group Databasebeta

C2×#29507597 #44509864

order30848
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#29507597

Splittings

SylowC241 ⋊ C2×#386

Subgroups

subgroupG/H
centerC24C22×D241
commutatorC22×C241C23×C4
FrattiniC23C23×D241
Fitting, prime radicalC23×D4×C241C2
socleC24×C241C23
cosocleC23×C241C24
hypercenterC23×D4D241
hypocenterC241C2×#386
LCSG ▷ C22×C241 ▷ C241
UCSC1 ◁ C24 ◁ C23×D4

1576 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15424

Conjugacy classes & character table

4856 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30848, 6929);