Finite Group Databasebeta

C2×#29504705 #44487781

order30592
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#29504705

Splittings

SylowC239 ⋊ C2×#398

Subgroups

subgroupG/H
centerC24C22×D239
commutator, cosocleC23×C239C24
FrattiniC23C23×D239
FittingC22×C4⋊C4×C239C2
socle, prime radicalC24×C239C23
hypercenterC22×C4⋊C4D239
hypocenterC239C2×#398
LCSG ▷ C23×C239 ▷ C239
UCSC1 ◁ C24 ◁ C22×C4⋊C4

692 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 30592

Conjugacy classes & character table

4804 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30592, 7743);