Finite Group Databasebeta

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C4×C7⋊C9×C67 #30683034

order16884
isoclinismisoclinic class of ΓL(1,𝔽8)
automorphism?
homologyAbelianization (H1) = C4×C9×C67 · Schur multiplier (H2) = C1

Aliases

direct productC4×C7⋊C9×C67
unambiguous semidirect product(C4×C7)⋊(C9×C67)

Splittings

derived, SylowC7 ⋊ C4×C9×C67
HallC4×C7×C67 ⋊ C9
HallC7×C67 ⋊ C4×C9
HallC4×C7 ⋊ C9×C67

Subgroups

subgroupG/H
center, hypercenterC3×C4×C67ΓL(1,𝔽8)
commutator, hypocenterC7C4×C9×C67
FrattiniC2×C3C2×ΓL(1,𝔽8)×C67
FittingC3×C4×C7×C67C3
socle, prime radicalC2×C3×C7×C67C2×C3
cosocleC2×C3×C7C2×C3×C67
LCSG ▷ C7
UCSC1 ◁ C3×C4×C67

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16884

Conjugacy classes & character table

4020 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16884, 3);