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C7×#18012818 #46799262

order33852
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×#18012818

Splittings

derived, HallC13×C31 ⋊ C3×C4×C7
HallC7×Dic403 ⋊ C3
HallC7×C31×C13⋊C3 ⋊ C4
HallC7×C13×C31 ⋊ C3×C4
HallDic403 ⋊ C3×C7
HallC31×C13⋊C3 ⋊ C4×C7
HallC7×C13⋊C3 ⋊ Dic31
HallC7×C31 ⋊ Dic13⋊C3
HallC7×C13 ⋊ C3×Dic31
HallC13⋊C3 ⋊ C7×Dic31
SylowC31 ⋊ C7×Dic13⋊C3
SylowC13 ⋊ C3×C7×Dic31

Subgroups

subgroupG/H
center, hypercenterC2×C7(C13⋊C3)⋊D31
commutator, hypocenterC13×C31C3×C4×C7
FrattiniC2C7×(C13⋊C3)⋊D31
Fitting, socleC2×C7×C13×C31C2×C3
prime radicalC2×C7×C31×C13⋊C3C2
cosocleC2×C13×C31C2×C3×C7
LCSG ▷ C13×C31
UCSC1 ◁ C2×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11284

Conjugacy classes & character table

1582 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33852, 57);