Finite Group Databasebeta

C2×#21440713 #29508731

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

Aliases

direct productC2×#21440713

Splittings

SylowC241 ⋊ C2×#108

Subgroups

subgroupG/H
centerC22C4⋊#11757210
commutatorC4×C241C22×C4
FrattiniC4C22×#11757210
FittingC2×C8×C241C4
socleC22×C241C4⋊C4
prime radicalC22×D241Q8
cosocleC4×D241C23
hypercenterC2×C8#11757210
hypocenterC241C2×#108
LCSG ▷ C4×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7712

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15424, 1563);