Finite Group Databasebeta

C2×#22560079 #30853776

order17152
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26

Aliases

direct productC2×#22560079

Splittings

SylowC67 ⋊ C2×#1770

Subgroups

subgroupG/H
centerC23×C4C22×D67
commutatorC22×C67C22×C42
FrattiniC22×C4C23×D67
FittingC22×C4⋊C8×C67C2
socle, prime radicalC24×C67C22×C4
cosocleC22×C4×C67C24
hypercenterC22×C4⋊C8D67
hypocenterC67C2×#1770
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23×C4 ◁ C22×C4⋊C8

1310 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17152

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, 167513);