Finite Group Databasebeta

C2×#21440703 #29508701

order15424
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#21440703

Splittings

SylowC241 ⋊ C2×#101

Subgroups

subgroupG/H
centerC22C22⋊#11757210
commutatorC22×C241C22×C4
FrattiniC22C22×#11757210
FittingC22×C4×C241C4
socleC22×C241C22⋊C4
prime radicalC23×C241C2×C4
cosocleC2×Dic241C23
hypercenterC22×C4#11757210
hypocenterC241C2×#101
LCSG ▷ C22×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7712

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15424, 1533);