Finite Group Databasebeta

C2×#22560413 #30856613

order17152
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#22560413

Splittings

SylowC67 ⋊ C2×#1855

Subgroups

subgroupG/H
centerC22×C4C2×C22⋊D67
commutatorC2×C4×C67C23×C4
FrattiniC22×C4C23×D67
FittingC2×#407×C67C2
socleC23×C67C2×C4⋊C4
prime radicalC25×C67Q8
cosocleC22×C4×C67C24
hypercenterC2×#407D67
hypocenterC67C2×#1855
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ C2×#407

1470 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

Conjugacy classes & character table

1924 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 170350);