Finite Group Databasebeta

C4×D4⋊#92418 #29570605

order15616
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4

Aliases

direct productC4×D4⋊#92418

Splittings

SylowC61 ⋊ C4×D4⋊C8

Subgroups

subgroupG/H
centerC2×C42C22⋊D61
commutatorC4×C61C2×C4×C8
FrattiniC2×C42C22×D61
FittingC42×D4×C61C2
socleC23×C61C2×C22⋊C4
prime radicalC22×D4×C61C2×C4
cosocleC2×C42×C61C23
hypercenterC42×D4D61
hypocenterC61C4×D4⋊C8
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C42 ◁ C43 ◁ C42×D4

774 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7808

Conjugacy classes & character table

2512 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 60160);