Finite Group Databasebeta

C2×#22569119 #31720144

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

Aliases

direct productC2×#22569119

Splittings

SylowC67 ⋊ C2×#2956

Subgroups

subgroupG/H
centerC2×C4C2×D4×D67
commutatorC4×C67C24×C4
FrattiniC2×C4C24×D67
Fitting, prime radicalC2×#575×C67C2
socleC22×C67C2×C4×D4
cosocleC2×C4×C67C25
hypercenterC2×#575D67
hypocenterC67C2×#2956
LCSG ▷ C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#575

2674 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2144

Conjugacy classes & character table

1540 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 1033881);