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C13⋊C3×C7⋊Dic35 #50303668

order38220
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C7

Aliases

direct productC13⋊C3×C7⋊Dic35

Splittings

derived, HallC5×C72×C13 ⋊ C3×C4
HallC13×C7⋊Dic35 ⋊ C3
HallC5×C72×C13⋊C3 ⋊ C4
HallC72×C13⋊C3 ⋊ Dic5
HallC72×C13 ⋊ C3×Dic5
HallC5×C72 ⋊ C4×C13⋊C3
HallC5×C13⋊C3 ⋊ C7⋊Dic7
HallC5×C13 ⋊ C3×C7⋊Dic7
SylowC72 ⋊ Dic5×C13⋊C3
SylowC13 ⋊ C3×C7⋊Dic35
SylowC5 ⋊ C13⋊C3×C7⋊Dic7

Subgroups

subgroupG/H
center, Frattini, hypercenterC2C13⋊C3×C5⋊(C7⋊D7)
commutator, hypocenterC5×C72×C13C3×C4
Fitting, socle, cosocleC2×C5×C72×C13C2×C3
prime radicalC2×C5×C72×C13⋊C3C2
LCSG ▷ C5×C72×C13
UCSC1 ◁ C2

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12740

Conjugacy classes & character table

1736 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 354);