Finite Group Databasebeta

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C3×C7×Dic97⋊C3 #37567819

order24444
automorphism?
homologyAbelianization (H1) = C32×C4×C7 · Schur multiplier (H2) = C3

Aliases

direct productC3×C7×Dic97⋊C3
unambiguous semidirect productDic97⋊(C32×C7)
unambiguous semidirect product(C3×Dic97)⋊(C3×C7)

Splittings

derived, SylowC97 ⋊ C32×C4×C7
HallC3×C7×C97⋊C3 ⋊ C4
HallC7×Dic97 ⋊ C32
HallC3×C97⋊C3 ⋊ C4×C7
HallC7×C97 ⋊ C32×C4
HallDic97 ⋊ C32×C7

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7D97⋊C3
commutator, hypocenterC97C32×C4×C7
FrattiniC2C3×C7×D97⋊C3
Fitting, socleC2×C3×C7×C97C2×C3
prime radicalC2×C3×C7×C97⋊C3C2
cosocleC2×C97C2×C32×C7
LCSG ▷ C97
UCSC1 ◁ C2×C3×C7

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8148

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24444, 82);