Finite Group Databasebeta

C2×#22560179 #30855166

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

Aliases

direct productC2×#22560179

Splittings

SylowC67 ⋊ C2×#1795

Subgroups

subgroupG/H
centerC22#16863252
commutatorC2×C4×C67C23×C4
FrattiniC22×C4C23×D67
Fitting, prime radicalC22×H(5,𝔽2)×C67C2
socleC22×C67#379
cosocleC22×C4×C67C24
hypercenterC22×H(5,𝔽2)D67
hypocenterC67C2×#1795
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×H(5,𝔽2)

3946 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2144

Conjugacy classes & character table

2302 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 168903);