Finite Group Databasebeta

C2×C4×#14523959 #30853498

order17152
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×C4×#14523959

Splittings

FittingC2×C4×M16×C67 ⋊ C2
SylowC67 ⋊ C2×C4×#100

Subgroups

subgroupG/H
centerC22×C4(C2×D67)⋊C4
commutatorC22×C67C22×C42
FrattiniC22×C4C23×D67
FittingC2×C4×M16×C67C2
socleC23×C67C2×C22⋊C4
prime radicalC23×D268C22
cosocleC22×C4×C67C24
hypercenterC2×C4×M16D67
hypocenterC67C2×C4×#100
LCSG ▷ C22×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×C4×M16

1970 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, 167235);