Finite Group Databasebeta

C2×C4×#14519684 #29601082

order15616
automorphism?
homologyAbelianization (H1) = C2×C43 · Schur multiplier (H2) = C26×C42

Aliases

direct productC2×C4×#14519684

Splittings

SylowC61 ⋊ C2×C4×#95

Subgroups

subgroupG/H
centerC24×C4C2×D61
commutatorC2×C61C2×C43
FrattiniC24C23×D61
FittingC23×C42×C61C2
socle, prime radicalC25×C61C23
cosocleC24×C61C24
hypercenterC23×C42D61
hypocenterC61C2×C4×#95
LCSG ▷ C2×C61 ▷ C61
UCSC1 ◁ C24×C4 ◁ C23×C42

4462 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15616

Conjugacy classes & character table

4000 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 90637);