Finite Group Databasebeta

C2×#26044197 #37554232

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

Aliases

direct productC2×#26044197

Splittings

SylowC367 ⋊ C2×#108

Subgroups

subgroupG/H
centerC2×C4D1468
commutatorC4×C367C22×C4
FrattiniC2×C4C22×D367
FittingC22×C8×C367C2
socleC22×C367C4⋊C4
prime radicalC23×C367Q8
cosocleC2×C4×C367C23
hypercenterC22×C8D367
hypocenterC367C2×#108
LCSG ▷ C4×C367 ▷ C2×C367 ▷ C367
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11744

Conjugacy classes & character table

5884 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23488, 595);