Finite Group Databasebeta

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C4×#16863523 #30854451

order17152
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productC4×#16863523

Splittings

SylowC67 ⋊ C4×#446

Subgroups

subgroupG/H
centerC2×C42C22×D67
commutatorC22×C67C22×C42
FrattiniC22×C4C23×D67
FittingC4×C4⋊C8×C67C2
socle, prime radicalC23×C67C23×C4
cosocleC22×C4×C67C24
hypercenterC4×C4⋊C8D67
hypocenterC67C4×#446
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C2×C42 ◁ C4×C4⋊C8

958 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, 168188);