Finite Group Databasebeta

C2×#29504700 #44487775

order30592
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#29504700

Splittings

SylowC239 ⋊ C2×#397

Subgroups

subgroupG/H
centerC24C22×D239
commutator, cosocleC23×C239C24
FrattiniC23C23×D239
FittingC22×C22⋊C4×C239C2
socleC24×C239C23
prime radicalC25×C239C22
hypercenterC22×C22⋊C4D239
hypocenterC239C2×#397
LCSG ▷ C23×C239 ▷ C239
UCSC1 ◁ C24 ◁ C22×C22⋊C4

820 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15296

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, 7737);