Finite Group Databasebeta

C4×#16863119 #30746334

order17152
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4

Aliases

direct productC4×#16863119

Splittings

FittingC4×C22⋊C8×C67 ⋊ C2
SylowC67 ⋊ C4×#323

Subgroups

subgroupG/H
centerC22×C4(C2×D67)⋊C4
commutatorC22×C67C2×C4×C8
FrattiniC23×C4C22×D67
FittingC4×C22⋊C8×C67C2
socleC23×C67C2×C22⋊C4
prime radicalC24×D67C2×C4
cosocleC23×C4×C67C23
hypercenterC4×C22⋊C8D67
hypocenterC67C4×#323
LCSG ▷ C22×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×C22⋊C8

946 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

Conjugacy classes & character table

2728 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 60071);