Finite Group Databasebeta

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C7×Dic5×C29⋊C7 #43249281

order28420
automorphism?
homologyAbelianization (H1) = C4×C72 · Schur multiplier (H2) = C7

Aliases

direct productC7×Dic5×C29⋊C7
unambiguous semidirect product(Dic5×C29)⋊C72
unambiguous semidirect product(C7×Dic5×C29)⋊C7

Splittings

derived, HallC5×C29 ⋊ C4×C72
HallC5×C7×C29⋊C7 ⋊ C4
HallDic5×C29 ⋊ C72
SylowC29 ⋊ C72×Dic5
SylowC5 ⋊ C4×C7×C29⋊C7

Subgroups

subgroupG/H
center, hypercenterC2×C7D5×C29⋊C7
commutator, hypocenterC5×C29C4×C72
FrattiniC2C7×D5×C29⋊C7
Fitting, socleC2×C5×C7×C29C2×C7
prime radicalC2×C5×C7×C29⋊C7C2
cosocleC2×C5×C29C2×C72
LCSG ▷ C5×C29
UCSC1 ◁ C2×C7

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4060

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28420, 56);