Finite Group Databasebeta

#97×C67⋊C8 #30745182

order17152
automorphism?
homologyAbelianization (H1) = C42×C8 · Schur multiplier (H2) = C2×C42

Aliases

direct product#97×C67⋊C8

Splittings

SylowC67 ⋊ C8×#97

Subgroups

subgroupG/H
center, FrattiniC2×C42C22×D67
commutatorC2×C67C42×C8
FittingC4×#97×C67C2
socle, prime radicalC23×C67C2×C42
cosocleC2×C42×C67C23
hypercenterC4×#97D67
hypocenterC67C8×#97
LCSG ▷ C2×C67 ▷ C67
UCSC1 ◁ C2×C42 ◁ C4×#97

606 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17152

Conjugacy classes & character table

2800 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 58919);