Finite Group Databasebeta

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#64423⋊C2 #10596889

order588
isoclinismisoclinic class of #64423⋊C2
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect product#64423⋊C2
unambiguous semidirect product#64424⋊C2

Splittings

Fitting, socle, derived, SylowC72 ⋊ C22×C3
HallD72 ⋊ C3
Hall#3861 ⋊ C22

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC72C22×C3
LCSG ▷ C72
UCSC1

52 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14

Polycyclic presentation:

2^2,3,7^2|e^a=e^6,d^b=d^6,d^c=d^2,e^c=e^2

Conjugacy classes & character table

19 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(#5997⋊C2)⋊C3, C2×#64423⋊C2, (#64418⋊C2)⋊C3, …
maximal normal subgroup of(#5997⋊C2)⋊C3, C2×#64423⋊C2, AGL(1,𝔽7)2, …
maximal quotient of#64423⋊C4, #11924174, #11924175, …
holomorph ofD7

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(588, 37);