Finite Group Databasebeta

C2×C4×#14524019 #31014275

order17152
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×C4×#14524019

Splittings

FittingC22×C4×Q8×C67 ⋊ C2
SylowC67 ⋊ C2×C4×C22⋊Q8

Subgroups

subgroupG/H
centerC23×C4C22×D67
commutatorC22×C67C24×C4
FrattiniC23C24×D67
FittingC22×C4×Q8×C67C2
socleC24×C67C24
prime radicalC24×D67C23
cosocleC23×C67C25
hypercenterC22×C4×Q8D67
hypocenterC67C2×C4×C22⋊Q8
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23×C4 ◁ C22×C4×Q8

3854 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

2752 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 328012);