Finite Group Databasebeta

C2×D4×D61⋊C8 #30625341

order15616
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C210

Aliases

direct productC2×D4×D61⋊C8
unambiguous semidirect productD61⋊(C2×C8×D4)

Splittings

SylowC61 ⋊ C22×C8×D4

Subgroups

subgroupG/H
centerC22×C4C22×#6923
commutatorC2×C61C24×C8
FrattiniC22C24×#6923
FittingC2×C4×D4×C61C4
socleC23×C61C23×C4
prime radicalC22×D4×D61C4
cosocleC2×Dic61C25
hypercenterC2×C4×D4#6923
hypocenterC61C22×C8×D4
LCSG ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C4×D4

3694 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1114896);