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C3×C3⋊(C7⋊Dic133) #45691965

order33516
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C7

Aliases

direct productC3×C3⋊(C7⋊Dic133)
unambiguous semidirect productC3⋊(C3×C7⋊Dic133)

Splittings

derivedC3×C72×C19 ⋊ C3×C4
HallC32×C72×C19 ⋊ C4
HallC72×C19 ⋊ C3×Dic3
HallC32×C72 ⋊ Dic19
HallC32×C19 ⋊ C7⋊Dic7
SylowC72 ⋊ C3×Dic57
SylowC19 ⋊ C3×C3⋊(C7⋊Dic7)
SylowC32 ⋊ C7⋊Dic133

Subgroups

subgroupG/H
center, hypercenterC2×C3C3⋊(C7⋊D133)
commutator, hypocenterC3×C72×C19C3×C4
FrattiniC2C3×C3⋊(C7⋊D133)
Fitting, socle, prime radicalC2×C32×C72×C19C2
cosocleC2×C3×C72×C19C2×C3
LCSG ▷ C3×C72×C19
UCSC1 ◁ C2×C3

280 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11172

Conjugacy classes & character table

8388 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 763);