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C7×C3⋊#13089712 #44479015

order30492
automorphism?
homologyAbelianization (H1) = C4×C7 · Schur multiplier (H2) = C3

Aliases

direct productC7×C3⋊#13089712
unambiguous semidirect productC3⋊(C7×#13089712)

Splittings

derived, HallC3×C112⋊C3 ⋊ C4×C7
HallC3×C7×C112⋊C3 ⋊ C4
HallC7×C112 ⋊ C3⋊Dic3
SylowC112 ⋊ C7×C3⋊Dic3

Subgroups

subgroupG/H
center, hypercenterC2×C7C3⋊#10624391
commutator, hypocenterC3×C112⋊C3C4×C7
FrattiniC2C7×C3⋊#10624391
Fitting, socleC2×C3×C7×C112D3
prime radicalC2×C3×C7×C112⋊C3C2
cosocleC2×C3×C112⋊C3C2×C7
LCSG ▷ C3×C112⋊C3
UCSC1 ◁ C2×C7

104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2772

Conjugacy classes & character table

1134 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30492, 238);