Finite Group Databasebeta

#108×D367 #37554230

order23488
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct product#108×D367

Splittings

Fitting#108×C367 ⋊ C2
SylowC367 ⋊ C2×#108

Subgroups

subgroupG/H
centerC4D4×D367
commutatorC4×C367C22×C4
FrattiniC2×C4C22×D367
Fitting#108×C367C2
socleC2×C367C2×C4⋊C4
prime radicalC22×D367Q8
cosocleC2×C4×C367C23
hypercenter#108D367
hypocenterC367C2×#108
LCSG ▷ C4×C367 ▷ C2×C367 ▷ C367
UCSC1 ◁ C4 ◁ C2×C4 ◁ #108

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5872

Conjugacy classes & character table

2590 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23488, 593);