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C3×C7⋊#13184068 #49153166

order37380
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7⋊#13184068

Splittings

Fitting, socle, HallC3×C5×C7×C89 ⋊ C4
derived, HallC5×C7×C89 ⋊ C3×C4
HallC3×C7×C89 ⋊ AGL(1,𝔽5)
HallC3×C5×C89 ⋊ Dic7
HallC7×C89 ⋊ C3×AGL(1,𝔽5)
HallC5×C89 ⋊ C3×Dic7
HallC3×C89 ⋊ C7⋊AGL(1,𝔽5)
HallC3×C5×C7 ⋊ #67063
SylowC89 ⋊ C3×C7⋊AGL(1,𝔽5)
HallC5×C7 ⋊ C3×#67063
HallC3×C7 ⋊ #13184068
HallC3×C5 ⋊ C7⋊#67063
SylowC7 ⋊ C3×#13184068
SylowC5 ⋊ C3×C7⋊#67063

Subgroups

subgroupG/H
center, hypercenterC3C7⋊#13184068
commutator, hypocenterC5×C7×C89C3×C4
FrattiniC1G
Fitting, socleC3×C5×C7×C89C4
prime radicalC3×C7×D445C2
cosocleC7×D445C2×C3
LCSG ▷ C5×C7×C89
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9345

Conjugacy classes & character table

2361 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37380, 60);