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C2×C4×#14524042 #31014351

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

Aliases

direct productC2×C4×#14524042

Splittings

SylowC67 ⋊ C2×C4×C4⋊Q8

Subgroups

subgroupG/H
centerC23×C4C22×D67
commutatorC22×C67C24×C4
FrattiniC23C24×D67
FittingC2×C4×C4⋊C4×C67C2
socle, prime radicalC24×C67C24
cosocleC23×C67C25
hypercenterC2×C4×C4⋊C4D67
hypocenterC67C2×C4×C4⋊Q8
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23×C4 ◁ C2×C4×C4⋊C4

3358 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, 328088);