Finite Group Databasebeta

C2×C4×#14524049 #31719232

order17152
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×C4×#14524049

Splittings

FittingC22×C4×C8×C67 ⋊ C2
SylowC67 ⋊ C2×C4×#131

Subgroups

subgroupG/H
centerC2×C4×C8C2×D67
commutatorC2×C67C23×C42
FrattiniC2×C4C24×D67
FittingC22×C4×C8×C67C2
socleC23×C67C23×C4
prime radicalC22×#11761628C22
cosocleC2×C4×C67C25
hypercenterC22×C4×C8D67
hypocenterC67C2×C4×#131
LCSG ▷ C2×C67 ▷ C67
UCSC1 ◁ C2×C4×C8 ◁ C22×C4×C8

3366 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

4384 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 1032969);