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C4×#16863562 #30861701

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

Aliases

direct productC4×#16863562

Splittings

FittingC4×AGL(1,ℤ/8)×C67 ⋊ C2
SylowC67 ⋊ C4×#453

Subgroups

subgroupG/H
centerC2×C4#14524011
commutatorC2×C4×C67C23×C4
FrattiniC22×C4C23×D67
FittingC4×AGL(1,ℤ/8)×C67C2
socleC22×C67C2×#120
prime radicalC2×#16863562C2
cosocleC22×C4×C67C24
hypercenterC4×AGL(1,ℤ/8)D67
hypocenterC67C4×#453
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×AGL(1,ℤ/8)

1578 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2144

Conjugacy classes & character table

1516 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 175438);