Finite Group Databasebeta

#108×D379 #37565288

order24256
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct product#108×D379

Splittings

Fitting#108×C379 ⋊ C2
SylowC379 ⋊ C2×#108

Subgroups

subgroupG/H
centerC4D4×D379
commutatorC4×C379C22×C4
FrattiniC2×C4C22×D379
Fitting#108×C379C2
socleC2×C379C2×C4⋊C4
prime radicalC22×D379Q8
cosocleC2×C4×C379C23
hypercenter#108D379
hypocenterC379C2×#108
LCSG ▷ C4×C379 ▷ C2×C379 ▷ C379
UCSC1 ◁ C4 ◁ C2×C4 ◁ #108

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6064

Conjugacy classes & character table

2674 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24256, 593);