Finite Group Databasebeta

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#537×C277 #31799671

order17728
nilpotency class2
isoclinismisoclinic class of #534
automorphism?
homologyAbelianization (H1) = C24×C277 · Schur multiplier (H2) = C25

Aliases

direct product#537×C277

Subgroups

subgroupG/H
center, socleC22×C277C24
commutator, Frattini, cosocleC22C24×C277
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C277 ◁ G

294 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8864

Conjugacy classes & character table

6094 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#47982102, #47982136, #47982170, …
maximal subgroup of#1598×C277, #1604×C277, #1610×C277, …
maximal normal subgroup of#1598×C277, #1604×C277, #1610×C277, …
maximal quotient of#2311×C277, #2316×C277, #2323×C277, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17728, 218);