Finite Group Databasebeta

C2×#29504652 #44486967

order30592
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#29504652

Splittings

SylowC239 ⋊ C2×#386

Subgroups

subgroupG/H
centerC24C22×D239
commutatorC22×C239C23×C4
FrattiniC23C23×D239
Fitting, prime radicalC23×D4×C239C2
socleC24×C239C23
cosocleC23×C239C24
hypercenterC23×D4D239
hypocenterC239C2×#386
LCSG ▷ C22×C239 ▷ C239
UCSC1 ◁ C24 ◁ C23×D4

1576 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15296

Conjugacy classes & character table

4816 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30592, 6929);