Finite Group Databasebeta

#390×D239 #44487001

order30592
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C4

Aliases

direct product#390×D239

Splittings

Fitting#390×C239 ⋊ C2
SylowC239 ⋊ C2×#390

Subgroups

subgroupG/H
center, FrattiniC23C23×D239
commutatorC22×C239C23×C4
Fitting#390×C239C2
socle, cosocleC23×C239C24
prime radicalC22×D4×D239C2
hypercenter#390D239
hypocenterC239C2×#390
LCSG ▷ C22×C239 ▷ C239
UCSC1 ◁ C23 ◁ #390

1360 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, 6963);