Finite Group Databasebeta

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C7×C13⋊C3×Dic21 #37524765

order22932
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×C13⋊C3×Dic21
unambiguous semidirect productC3⋊(C7×Dic7×C13⋊C3)

Splittings

derivedC3×C7×C13 ⋊ C3×C4×C7
HallC3×C72×C13⋊C3 ⋊ C4
HallC72×C13 ⋊ C3×Dic3
HallC3×C13⋊C3 ⋊ C7×Dic7
SylowC72 ⋊ Dic3×C13⋊C3
SylowC13 ⋊ C3×C7×Dic21

Subgroups

subgroupG/H
center, hypercenterC2×C7C13⋊C3×D21
commutator, hypocenterC3×C7×C13C3×C4×C7
FrattiniC2C7×C13⋊C3×D21
Fitting, socleC2×C3×C72×C13C2×C3
prime radicalC2×C3×C72×C13⋊C3C2
cosocleC2×C3×C7×C13C2×C3×C7
LCSG ▷ C3×C7×C13
UCSC1 ◁ C2×C7

184 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1092

Conjugacy classes & character table

1176 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22932, 710);