Finite Group Databasebeta

#108×D479 #44500439

order30656
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct product#108×D479

Splittings

Fitting#108×C479 ⋊ C2
SylowC479 ⋊ C2×#108

Subgroups

subgroupG/H
centerC4D4×D479
commutatorC4×C479C22×C4
FrattiniC2×C4C22×D479
Fitting#108×C479C2
socleC2×C479C2×C4⋊C4
prime radicalC22×D479Q8
cosocleC2×C4×C479C23
hypercenter#108D479
hypocenterC479C2×#108
LCSG ▷ C4×C479 ▷ C2×C479 ▷ C479
UCSC1 ◁ C4 ◁ C2×C4 ◁ #108

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7664

Conjugacy classes & character table

3374 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30656, 593);