Finite Group Databasebeta

#108×D373 #37559466

order23872
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct product#108×D373

Splittings

Fitting#108×C373 ⋊ C2
SylowC373 ⋊ C2×#108

Subgroups

subgroupG/H
centerC4D4×D373
commutatorC4×C373C22×C4
FrattiniC2×C4C22×D373
Fitting#108×C373C2
socleC2×C373C2×C4⋊C4
prime radicalC22×D373Q8
cosocleC2×C4×C373C23
hypercenter#108D373
hypocenterC373C2×#108
LCSG ▷ C4×C373 ▷ C2×C373 ▷ C373
UCSC1 ◁ C4 ◁ C2×C4 ◁ #108

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5968

Conjugacy classes & character table

2632 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23872, 593);