Finite Group Databasebeta

C2×#29504656 #44486972

order30592
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#29504656

Splittings

SylowC239 ⋊ C2×#387

Subgroups

subgroupG/H
centerC24C22×D239
commutatorC22×C239C23×C4
FrattiniC23C23×D239
FittingC22×C42×C239C2
socle, prime radicalC24×C239C23
cosocleC23×C239C24
hypercenterC22×C42D239
hypocenterC239C2×#387
LCSG ▷ C22×C239 ▷ C239
UCSC1 ◁ C24 ◁ C22×C42

712 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 30592

Conjugacy classes & character table

7672 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30592, 6934);