Finite Group Databasebeta

C2×#108×D23 #15681998

order2944
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#108×D23

Splittings

FittingC2×C23×#108 ⋊ C2
SylowC23 ⋊ C22×#108

Subgroups

subgroupG/H
centerC2×C4D4×D23
commutatorC4×C23C23×C4
FrattiniC2×C4C23×D23
FittingC2×C23×#108C2
socleC22×C23C2×C4⋊C4
prime radicalC23×D23Q8
cosocleC2×C4×C23C24
hypercenterC2×#108D23
hypocenterC23C22×#108
LCSG ▷ C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#108

480 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 736

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 13111);