Finite Group Databasebeta

#386×D239 #44486962

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

Aliases

direct product#386×D239

Splittings

Fitting#386×C239 ⋊ C2
SylowC239 ⋊ C2×#386

Subgroups

subgroupG/H
center, FrattiniC23C23×D239
commutatorC22×C239C23×C4
Fitting#386×C239C2
socle, cosocleC23×C239C24
prime radicalC22×D4×D239C2
hypercenter#386D239
hypocenterC239C2×#386
LCSG ▷ C22×C239 ▷ C239
UCSC1 ◁ C23 ◁ #386

1576 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7648

Conjugacy classes & character table

3388 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30592, 6924);