Finite Group Databasebeta

C2×#26044180 #37554166

order23488
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#26044180

Splittings

SylowC367 ⋊ C2×#101

Subgroups

subgroupG/H
centerC22C22⋊Dic367
commutatorC22×C367C22×C4
FrattiniC2×C4C22×D367
FittingC22×Q8×C367C2
socleC22×C367C22⋊C4
prime radicalC23×C367C2×C4
cosocleC2×C4×C367C23
hypercenterC22×Q8D367
hypocenterC367C2×#101
LCSG ▷ C22×C367 ▷ C2×C367 ▷ C367
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11744

Conjugacy classes & character table

3682 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23488, 529);