Finite Group Databasebeta

#108×D467 #44470081

order29888
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct product#108×D467

Splittings

Fitting#108×C467 ⋊ C2
SylowC467 ⋊ C2×#108

Subgroups

subgroupG/H
centerC4D4×D467
commutatorC4×C467C22×C4
FrattiniC2×C4C22×D467
Fitting#108×C467C2
socleC2×C467C2×C4⋊C4
prime radicalC22×D467Q8
cosocleC2×C4×C467C23
hypercenter#108D467
hypocenterC467C2×#108
LCSG ▷ C4×C467 ▷ C2×C467 ▷ C467
UCSC1 ◁ C4 ◁ C2×C4 ◁ #108

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7472

Conjugacy classes & character table

3290 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29888, 593);