Finite Group Databasebeta

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#41×#64424 #72245132

order4704
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C25

Aliases

direct product#41×#64424

Splittings

FittingC72×#41 ⋊ C2×C3
Hall#41×C7⋊D7 ⋊ C3
Hall#3861 ⋊ C2×#41
SylowC72 ⋊ C2×C3×#41

Subgroups

subgroupG/H
centerC4C22×#64424
commutator, socle, cosocleC2×C72C24×C3
FrattiniC2C23×#64424
FittingC72×#41C2×C3
hypercenter#41#64424
hypocenterC72C2×C3×#41
LCSG ▷ C2×C72 ▷ C72
UCSC1 ◁ C4 ◁ #41

1640 conjugacy classes of subgroups; only the 293 normal subgroups are shown.

normal subgroups only

This group has 1640 conjugacy classes of subgroups — too many to draw. Only its 293 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 392

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,ℤ/8)×#64424, #41×ΓL(1,𝔽8)⋊AGL(1,𝔽7), H(5,𝔽2)×#64424, …
maximal normal subgroup ofAGL(1,ℤ/8)×#64424, #41×ΓL(1,𝔽8)⋊AGL(1,𝔽7), H(5,𝔽2)×#64424, …
maximal quotient ofC2×#41×#64424, C4×D4×#64424

GAP

Past the SmallGroups library coverage — no SmallGroups id.