Finite Group Databasebeta

#108×C67⋊C8 #30747125

order17152
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4

Aliases

direct product#108×C67⋊C8

Splittings

SylowC67 ⋊ C8×#108

Subgroups

subgroupG/H
centerC42D4×D67
commutatorC4×C67C2×C4×C8
FrattiniC2×C42C22×D67
FittingC4×#108×C67C2
socleC22×C67C4×C4⋊C4
prime radicalC23×C67C4×Q8
cosocleC2×C42×C67C23
hypercenterC4×#108D67
hypocenterC67C8×#108
LCSG ▷ C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C42 ◁ C2×C42 ◁ C4×#108

374 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

1960 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 60862);