Finite Group Databasebeta

C2×#22560663 #30857613

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

Aliases

direct productC2×#22560663

Splittings

SylowC67 ⋊ C2×#1898

Subgroups

subgroupG/H
centerC23C2×C22⋊Dic67
commutatorC23×C67C23×C4
FrattiniC24C23×D67
Fitting, prime radicalC22×#120×C67C2
socleC23×C67C2×C22⋊C4
cosocleC24×C67C24
hypercenterC22×#120D67
hypocenterC67C2×#1898
LCSG ▷ C23×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C26 ◁ C22×#120

3746 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2144

Conjugacy classes & character table

1912 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 171350);