Finite Group Databasebeta

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C4×#16863520 #30854435

order17152
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct productC4×#16863520

Splittings

SylowC67 ⋊ C4×C8×Q8

Subgroups

subgroupG/H
centerC2×C42C22×D67
commutatorC2×C67C22×C4×C8
FrattiniC22×C4C23×D67
FittingC4×C4⋊C8×C67C2
socle, prime radicalC23×C67C23×C4
cosocleC22×C4×C67C24
hypercenterC4×C4⋊C8D67
hypocenterC67C4×C8×Q8
LCSG ▷ C2×C67 ▷ C67
UCSC1 ◁ C2×C42 ◁ C4×C4⋊C8

1070 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, 168172);