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C3×C7×#13184069 #49153164

order37380
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×#13184069

Splittings

Fitting, socle, HallC3×C5×C7×C89 ⋊ C4
derived, HallC5×C89 ⋊ C3×C4×C7
HallC5×C7×C89 ⋊ C3×C4
HallC3×C7×C89 ⋊ AGL(1,𝔽5)
HallC3×C5×C89 ⋊ C4×C7
HallC7×C89 ⋊ C3×AGL(1,𝔽5)
HallC3×C89 ⋊ C7×AGL(1,𝔽5)
HallC3×C5×C7 ⋊ Dic89
SylowC89 ⋊ C3×C7×AGL(1,𝔽5)
HallC5×C7 ⋊ C3×Dic89
HallC3×C5 ⋊ C7×Dic89
SylowC5 ⋊ C3×C7×Dic89

Subgroups

subgroupG/H
center, hypercenterC3×C7#13184069
commutator, hypocenterC5×C89C3×C4×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C89C4
prime radicalC3×C7×D5×C89C2
cosocleD5×C89C2×C3×C7
LCSG ▷ C5×C89
UCSC1 ◁ C3×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9345

Conjugacy classes & character table

3801 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37380, 58);