Finite Group Databasebeta

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C3×C3⋊(C7⋊Dic119) #44472693

order29988
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C7

Aliases

direct productC3×C3⋊(C7⋊Dic119)
unambiguous semidirect productC3⋊(C3×C7⋊Dic119)

Splittings

derivedC3×C72×C17 ⋊ C3×C4
HallC32×C72×C17 ⋊ C4
HallC72×C17 ⋊ C3×Dic3
HallC32×C72 ⋊ Dic17
HallC32×C17 ⋊ C7⋊Dic7
SylowC72 ⋊ C3×Dic51
SylowC17 ⋊ C3×C3⋊(C7⋊Dic7)
SylowC32 ⋊ C7⋊Dic119

Subgroups

subgroupG/H
center, hypercenterC2×C3C3⋊(C7⋊D119)
commutator, hypocenterC3×C72×C17C3×C4
FrattiniC2C3×C3⋊(C7⋊D119)
Fitting, socle, prime radicalC2×C32×C72×C17C2
cosocleC2×C3×C72×C17C2×C3
LCSG ▷ C3×C72×C17
UCSC1 ◁ C2×C3

280 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9996

Conjugacy classes & character table

7506 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29988, 334);