Finite Group Databasebeta

C4×(C2×D71)⋊C16 #31912480

order18176
automorphism?
homologyAbelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C23×C4

Aliases

direct productC4×(C2×D71)⋊C16

Splittings

FittingC2×C4×C16×C71 ⋊ C2
SylowC71 ⋊ C4×C22⋊C16

Subgroups

subgroupG/H
centerC2×C4×C8C2×D71
commutatorC2×C71C2×C4×C16
FrattiniC22×C8C22×D71
FittingC2×C4×C16×C71C2
socleC23×C71C22×C8
prime radicalC23×D71C2×C8
cosocleC22×C8×C71C23
hypercenterC2×C4×C16D71
hypocenterC71C4×C22⋊C16
LCSG ▷ C2×C71 ▷ C71
UCSC1 ◁ C2×C4×C8 ◁ C2×C4×C16

614 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9088

Conjugacy classes & character table

4640 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 84596);