Finite Group Databasebeta

#344×D239 #44484288

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

Aliases

direct product#344×D239

Splittings

Fitting#344×C239 ⋊ C2
SylowC239 ⋊ C2×#344

Subgroups

subgroupG/H
centerC4C22⋊C4×D239
commutatorC22×C239C2×C42
FrattiniC22×C4C22×D239
Fitting#344×C239C2
socleC2×C239C2×#95
prime radicalC23×D239C2×C4
cosocleC22×C4×C239C23
hypercenter#344D239
hypocenterC239C2×#344
LCSG ▷ C22×C239 ▷ C2×C239 ▷ C239
UCSC1 ◁ C4 ◁ C22×C4 ◁ #344

388 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3824

Conjugacy classes & character table

2662 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30592, 4250);