Finite Group Databasebeta

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C7×C3⋊(Dic97⋊C3) #37567831

order24444
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×C3⋊(Dic97⋊C3)
unambiguous semidirect productC3⋊(C7×Dic97⋊C3)
unambiguous semidirect productDic291⋊(C3×C7)

Splittings

derivedC3×C97 ⋊ C3×C4×C7
HallC3×C7×C97⋊C3 ⋊ C4
HallC3×C97⋊C3 ⋊ C4×C7
HallC7×C97 ⋊ C3×Dic3
SylowC97 ⋊ C3×C7×Dic3

Subgroups

subgroupG/H
center, hypercenterC2×C7C3⋊(D97⋊C3)
commutator, hypocenterC3×C97C3×C4×C7
FrattiniC2C7×C3⋊(D97⋊C3)
Fitting, socleC2×C3×C7×C97C2×C3
prime radicalC2×C3×C7×C97⋊C3C2
cosocleC2×C3×C97C2×C3×C7
LCSG ▷ C3×C97
UCSC1 ◁ C2×C7

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8148

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24444, 94);