Finite Group Databasebeta

C2×#29504540 #44484283

order30592
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#29504540

Splittings

SylowC239 ⋊ C2×#343

Subgroups

subgroupG/H
centerC23(C2×D239)⋊C4
commutatorC22×C239C2×C42
FrattiniC22×C4C22×D239
FittingC22×M16×C239C2
socleC23×C239C22⋊C4
prime radicalC24×C239C2×C4
cosocleC22×C4×C239C23
hypercenterC22×M16D239
hypocenterC239C2×#343
LCSG ▷ C22×C239 ▷ C2×C239 ▷ C239
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×M16

432 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, 4245);