Finite Group Databasebeta

← Prev (#30606650) Next (#30606652) →

C4⋊C16×#6923 #30606651

order15616
automorphism?
homologyAbelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4⋊C16×#6923

Splittings

FittingC61×C4⋊C16 ⋊ C4
SylowC61 ⋊ C4×C4⋊C16

Subgroups

subgroupG/H
center, FrattiniC2×C8C22×#6923
commutatorC2×C61C2×C4×C16
FittingC61×C4⋊C16C4
socleC22×C61C2×C4×C8
prime radicalC22×D61C22×C8
cosocleC2×C8×D61C23
hypercenterC4⋊C16#6923
hypocenterC61C4×C4⋊C16
LCSG ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C8 ◁ C4⋊C16

438 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, 1096206);