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Q82×C227 #28408722

order14528
nilpotency class2
automorphism?
homologyAbelianization (H1) = C24×C227 · Schur multiplier (H2) = C24

Aliases

direct productQ82×C227

Subgroups

subgroupG/H
center, socle, prime radicalC22×C227C24
commutator, Frattini, cosocleC22C24×C227
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C227 ◁ G

212 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14528

Conjugacy classes & character table

5675 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#44398812, #44398874, #44398955, …
maximal subgroup of#1623×C227, #1633×C227, #1645×C227, …
maximal normal subgroup of#1623×C227, #1633×C227, #1645×C227, …
maximal quotient ofQ8×C4⋊C4×C227, #2369×C227, #2451×C227, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14528, 239);